The concentration​ C(t) of a drug administered to a patient intravenously jumps to its highest level almost immediately. The concentration subsequently decays exponentially according to the law C(t)=C0e^-kt where C0=C(0). The physician adminstering the drug would like to have m


where m is the concentration below which the drug is ineffective and M is the concentration above which the drug is dangerous. The​ half-life of the drug is


hours. Suppose a patient receives


milligrams of the drug at

8 AM How much of the drug is in the​ patient's blood at 4

P.M. the same​ day?



At 4 PM _____ miligrams of the drug are in the patients blood????????

 Mar 25, 2020

C(t) = 17  e-kt       I will assume t  is hours

1/2 of the drug will be gone 28 hours   = 8.5 mg

8.5 mg  = 17 e-k(28)      yields  k = .0247553


8AM to 4 PM is  8 hours   = t


17 e-.0247553(8)  =  13.95 mg  still in pt at 4 pm

 Mar 25, 2020

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